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Homogeneity and composition of AlInGaN : a multiprobe nanostructure study

Reference:Krause Florian F., Ahl Jan-Philipp, Tytko Darius, Egoavil Escobar Ricardo Juan, Verbeeck Johan, et al..- Homogeneity andcomposition of AlInGaN : a multiprobe nanostructure studyUltramicroscopy - ISSN 0304-3991 - 156(2015), p. 29-36 DOI: http://dx.doi.org/doi:10.1016/j.ultramic.2015.04.012

Institutional repository IRUA

Homogeneity and Composition of AlInGaN:A Multiprobe Nanostructure Study

Florian F. Krausea,∗, Jan-Philipp Ahlb, Darius Tytkoc, Pyuck-Pa Choic,Ricardo Egoavild, Marco Schowaltera, Thorsten Mehrtensa, Knut

Muller-Casparya, Johan Verbeeckd, Dierk Raabec, Joachim Hertkornb, KarlEnglb, Andreas Rosenauera

aInstitut fur Festkorperphysik, Universitat Bremen, Otto-Hahn-Allee 1, 28359 Bremen,Germany

bOSRAM Opto Semiconductors GmbH, Leibnizstr. 4, 93055 Regensburg, GermanycMax-Planck-Institut fur Eisenforschung GmbH, Max-Planck-Str. 1, 40237 Dusseldorf ,

GermanydEMAT, Universiteit Antwerpen, Groenenborgerlaan 171, 2020 Antwerpen , Belgium

Abstract

The electronic properties of quaternary AlInGaN devices significantly dependon the homogeneity of the alloy. The identification of compositional fluctuationsor verification of random-alloy distribution is hence of grave importance. Here, acomprehensive multiprobe study of composition and compositional homogeneityis presented, investigating AlInGaN layers with indium concentrations rangingfrom 0 to 17 at.% and aluminum concentrations between 0 and 39 at.% em-ploying high-angle annular dark field scanning electron microscopy (HAADFSTEM), energy dispersive X-ray spectroscopy (EDX) and atom probe tomog-raphy (APT). EDX mappings reveal distributions of local concentrations whichare in good agreement with random alloy atomic distributions. This was henceinvestigated with HAADF STEM by comparison with theoretical random alloyexpectations using statistical tests. To validate the performance of these tests,HAADF STEM image simulations were carried out for the case of a random-alloy distribution of atoms and for the case of In-rich clusters with nanometerdimensions. The investigated samples, which were grown by metal-organic va-por phase epitaxy (MOVPE), were thereby found to be homogeneous on thisnanometer scale. Analysis of reconstructions obtained from APT measurementsyielded matching results. Though HAADF STEM only allows for the reductionof possible combinations of indium and aluminum concentrations to the prox-imity of isolines in the two-dimensional composition space. The observed rangesof composition are in good agreement with the EDX and APT results withinthe respective precisions.

Keywords: HAADF STEM, AlInGaN, Homogeneity, InAlGaN, EDX, APT

∗Corresponding authorEmail address: f.krause@ifp.uni-bremen.de (Florian F. Krause)

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1. Introduction

Quaternary AlInGaN has attracted increasing attention in the past yearsfor the design of blue light emitting diodes (LEDs) [1, 2] and field-effect tran-sistors (FETs) [3, 4]. The material benefits from its additional degree of free-dom opposed to ternary systems, which to a certain extent allows an indepen-dent choice of either bandgap and lattice constant, allowing for the realisationof lattice-matched structures, or bandgap and polarisation, enabling so-calledpolarisation-matched growth of AlInGaN/GaN heterostructures. In these struc-tures, polarisation effects such as the quantum-confined Stark effect are reduced,which is expected to lead to an increase in efficiency [5].

Besides the matching of polarisation, homogeneity of the alloy as well asdefect density and morphology of the interfaces govern the electronic propertiesof AlInGaN-based devices [6–9]. Spectral width and efficiency of the emis-sion of light from quantum wells (QWs) strongly depend on the distribution ofindium, aluminum and gallium atoms within the wells. Some publications re-ported observations of indium-rich cluster formation, catalysed by the presenceof aluminum in the quaternary material opposed to ternary InGaN [10, 11]. Mat-suoka [12] even found an unstable mixing region covering most of the quaternarycomposition space, whereas Marques et al. [13] predicted a phase transition fromclustering to homogeneous mixing behavior at ≈ 800 ◦C growth temperature.The present work demonstrates a comprehensive investigation of compositionalhomogeneity in AlInGaN layers grown by metal-organic vapour phase epitaxy(MOVPE) employing different high-resolution experimental methods, specif-ically, energy dispersive X-ray spectroscopy (EDX), high-angle annular darkfield scanning transmission electron microscopy (HAADF STEM) and atom-probe tomography (APT).

HAADF STEM has already successfully been used for the investigationof composition and compositional homogeneity in ternary materials such asAlGaN, InGaN or InAlN [14–16]. It benefits from the reduced beam dam-age compared to parallel illumination [15, 17]. For the quaternary materialAlxInyGa1−x−yN, however, measurement of indium and aluminum concentra-tions would require two separate inequivalent measured quantities. Thus, HAADFSTEM measurements alone do not allow for determination of the compositionin AlInGaN.

EDX, however, which is available during STEM measurements in modernelectron microscopes, makes the simultaneous determination of both concentra-tions possible. With high brightness electron sources, probe correctors and win-dowless four-quadrant X-ray detectors it can even reach atomic resolution today[18]. For the investigation of possible clustering on the nanometer scale, how-ever, long acquisition times are necessary to reach sufficient statistical signifi-cance, during which specimen drift can occur, cumbering the statistical analysis.Furthermore, as the resulting composition map is a two-dimensional projection

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of the specimen, in general corresponding simulations would be necessary tounderstand the exact volume of interaction in dependence of probe position.

APT-investigations overcome both disadvantages, as in these reconstructionsboth, the type and the initial position of each detected ion are determined,allowing for a three-dimensional investigation of the spatial distribution of allspecies with respect to all other species. The crystal volume which is accessiblein one measurement is, however, limited even compared to the nanometer-thinTEM-lamellas due to the sharp needle shape of the APT specimen.

In the following, a comprehensive study of composition and homogeneityof AlInGaN with various concentrations using all methods mentioned above ispresented. Samples with nominal compositions as listed in Tab. 1, comprisinglayers with four different aluminum concentrations between 0 and 39 at.% and12 at.% In as well as AlGaN layers with nominal 39 at.% Al were investigated.

2. Specimens and Instrumentation

The specimen primarily investigated here consists of 5 consecutive layersof AlInGaN of different concentrations embedded in GaN. It was grown byMOVPE on GaN/sapphire templates. Each layer is ≈ 10 nm thick and is sep-arated from the next layer by a barrier of ≈ 50 nm GaN. They were grown farfrom thermodynamic equilibrium [19] at a temperature of 760 ◦C and a pres-sure of 200 hPa. A more detailed description of the growth and investigationof the surface morphology is given in the publication of Ahl et al. [20]. Two ofthe layers consist of InGaN and AlGaN, respectively, providing ternary refer-ences for the investigations. Single-layer specimens with thicker layers but withthe same nominal compositions were grown under identical conditions. Thesesamples were used for the EDX measurements as they provide larger areas forsimultaneous data acquisition within rectangular shaped areas of interest.

The first four compositions in Tab. 1 were pre-characterised by X-ray pho-toelectron spectroscopy (XPS) and photoluminescence spectroscopy (PL) [20].The concentrations determined by XPS are also given in Tab. 1, whereas thespectra gained from the PL-measurement are depicted in Fig. 1. Besides theexpected blue-shift for increasing aluminum concentrations, a broadening of thequaternary luminescence peak is observed. In the present paper, it is investi-gated, whether this increasing width is solely caused by the local concentrationfluctuations inevitably occurring in a random alloy, which increase with thenumber of different constituents, or whether in addition indium clustering con-tributes to this effect.

A very thin sample was conventionally prepared by mechanical grinding andsubsequent ion polishing for HAADF STEM, whereas for the EDX analyses,lamellas were prepared with a focused ion beam (FIB) using the lift-out method[21]. The samples were afterwards milled with low-energy Ar ions at 400 eV toremove etching damage [22]. The needle-shaped tip specimens for APT mea-surements were likewise prepared with a FIB using the lift-out method describedin Ref. [23] and sharpened while successively reducing the ion energy from 30 kVto 2 kV.

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Table 1: Nominal aluminum and indium concentrations of the five investigated compositionsand the values measured by the different methods. The given errors were estimated fromconsecutive measurements of the same sample.

[at.%] nom. XPS [20] EDX APTAl In Al In Al In Al In

no.1 0 12 0± 0 13± 1 0± 0 10± 4 0± 0 12± 2no.2 13 12 13± 1 18± 1 17± 3 14± 3 16± 2 16± 2no.3 22 12 22± 1 20± 1 23± 3 16± 3 25± 2 16± 2no.4 39 12 39± 1 19± 1 33± 3 14± 3 31± 2 17± 2no.5 39 0 - - 39± 3 0± 0 36± 2 0± 0

Figure 1: PL-spectra of compositions no.1 to 4: Besides a blue-shift of the quaternary peakwith rising aluminum content an increase of the peak-width can be observed. While the ternarymaterial no.1 exhibits a full width at half maximum of 10 nm this increases to ≈ 27 nm forthe composition with the highest aluminum content. The oscillations for wavelengths aboveto the GaN peak are caused by Fabry-Perot interference in the GaN substrate.

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EDX-maps were recorded with the XAntEM microscope of the Universityof Antwerp, a cubed FEI Titan3 60/300 G2 TEM with ChemiSTEM-designequipped with a high-brightness X-FEG, a probe aberration corrector and awindowless Super-X EDX-detector, which was operated at 300 kV. The HAADFSTEM investigations were performed at a FEI Titan 80/300 G1 microscope alsooperated at 300 kV and equipped with a Fischione Model 3000 HAADF detectorspanning from 30 to approximately 250 mrad. Atom probe tomography wasconducted using a Cameca LEAP 3000X HR instrument.

3. Results and Discussion

3.1. EDX-Investigation

First, the single-layer specimens with layers of the nominal compositionsgiven in Tab. 1 and a thickness of (20± 5) nm were investigated by EDX. Allsamples were prepared as lamellas with a thickness of (40± 10) nm. EDX mapswere acquired by drift-corrected, repetitive scanning of an area as shown inFig. 2a for the quaternary specimen with the highest nominal aluminum con-centration (no.4 in Tab. 1), for which inhomogeneities are most likely to oc-cur [12, 13]. The scan time was chosen 10 min per spectrum-image with a pixelwidth of 6 A to obtain a sufficiently high detection count rate for accurate quan-tification. For this the Cliff-Lorimer method [24] implemented in the proprietaryBruker ESPRIT software was used to evaluate the K-Lines of aluminum andgallium and the indium L-line with calculated k-factors of 1.00, 2.11 and 3.05,respectively, while the background subtraction was done with a polynomial fitfrom chosen background windows.

The resulting mean concentrations from averaging over the entire layer areaare presented in Tab. 1, showing a generally good agreement with the nominalvalues. Fig. 2b displays the resulting composition map for the aluminum-richsample with composition no.4, which reveals an apparently homogeneous dis-tribution of In, Al and Ga. To investigate the distributions quantitatively,histograms of the relative frequencies of local In, Al and Ga concentrationswere generated from the composition maps. They are shown in Fig. 2c for themap in Fig. 2b and for the ternary InGaN layer (composition no.1) in Fig. 2dfor comparison. Using the mean concentration values determined by EDX inTab. 1 as probabilities to detect In, Al and Ga atoms, a theoretical distributionof concentrations was calculated by 100 independent random draws per pixel,each of which results in the detection of either indium, aluminum or gallium.The number of draws was chosen to match the ternary sample best. It roughlycorresponds to the number of atoms stacked in an atomic column at this spec-imen thickness. The binomial distributions, which represent ideal homogeneitydue to the mutual independence of the draws, are shown in Figs. 2c and das solid curves. Both samples show good agreement between measured andbinomial distributions, no increased deviation is observed for the quaternaryspecimen. Admittedly the assumption of a binomial distribution and especiallythe reasoned but still somewhat arbitrary choice of 100 draws, complicates the

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quantification of homogeneity from these data. For a less empirical model betterknowledge of the interaction volume of the electron beam within the specimen,of the X-ray propagation through the specimen and of the influence of detec-tion and spectrum-quantification procedures would be required. However, thegood representation of the experiment by the binomial model and the agreementbeing equally good for both the ternary and the quaternary sample, are clearindications for a homogeneous alloy, though the meaningfulness is limited dueto the mentioned lack of knowledge. Analogous evaluations were executed forboth other quaternary concentrations in Tab. 1 yielding similar results.

3.2. HAADF STEM Study

To further investigate the homogeneity of the AlInGaN alloys by statisticalmeans, HAADF STEM images of AlInGaN crystals were simulated for variousthicknesses with 31 at.% Al and 16 at.% In, corresponding to composition no.4in Tab. 1, where the metal atoms were set according to a completely randomdistribution. The simulations were conducted using the STEMsim softwarepackage [25] with the frozen-lattice multislice method [26, 27]. Static atomicdisplacements (SADs) caused by the different covalent radii of the metal atomswere incorporated by force relaxation with the LAMMPS program package [28]employing the empirical Stillinger-Weber type potential proposed by Schowalteret al. [29] for Al-N and Ga-N bonds, while for In-N interactions parametrisationfrom Ref. [30] was used. The nonuniform sensitivity of the HAADF detectorused in the following experiment was also taken into account [15]. The resultingimages, a section of which is displayed in Fig. 3a, were evaluated atomic-columnwise by averaging over Voronoi cells as described in Ref. [16]. To avoid dis-crepancies between experimental and simulated intensity distributions causedby slightly different mean concentrations, the intensities were divided by theirmean, thereby centering the histograms around 1, as shown in Fig. 3b. This isjustified, as the overall spread of intensities is less affected by small concentra-tion changes than the mean intensity.

The resulting intensity ratio distribution is visually in very good agreementwith a Gaussian distribution as can be seen in Fig. 3b. This agreement wasalso statistically tested: A chi-square goodness-of-fit test, which allows testingthe hypothesis that the simulated values come from a Gaussian distribution bycomparing the relative frequencies of simulation and ideal Gaussian distribution,confirms this hypothesis with a significance of 10% at all thicknesses. Theone-sample Kolmogorov-Smirnov-Lilliefors test [31], which is a modification ofthe well-known Kolmogorov-Smirnov test taking into account that mean andstandard deviation of the Gaussian distribution are not known in advance here,accepts even with 20% significance.

It shall be stressed here, that the statistical significance represents the prob-ability of erroneously rejecting the tested hypothesis, in this case that the un-derlying distribution is Gaussian. High significance does not necessarily imply,that the probability to only accept the hypothesis if it is true, which is calledthe statistical power of the test, is also high, though it is commonly used to

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Figure 2: Results of the EDX-investigation: (a) shows an HAADF STEM micrograph ofthe investigated area with the quaternary layer of composition no.4 marked. The intensityfluctuations are caused by contamination during the long acquisition time of 10 min. Theconcentration map is displayed color-coded in (b). From this, the histograms of indium, alu-minum and gallium concentrations presented in (c) were determined. (d) shows the histogramsfor the ternary InGaN sample (composition no.1) for comparison. The solid curves show thedistributions expected for a homogeneous alloy.

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Figure 3: HAADF STEM simulation of a random-alloy AlInGaN crystal with 31 at.% Aland 16 at.% In: In (a), a section of the image simulated for a specimen thickness of 2 nm isdepicted. The red polygon exemplifies a Voronoi cell. Intensities averaged in Voronoi cellsyield the histogram displayed in (b). The solid blue curve is the fitted Gaussian distribution.(c) depicts the standard deviation of the intensity ratio plotted vs. specimen thickness.

asses the results of a test. The test power has therefore also be checked whichis done later in this section.

The standard deviation of the simulated intensity ratio is plotted in Fig. 3c.For very thin crystals with thicknesses below 10 nm it is varying rapidly withthickness, but for thicker specimens the variation of the standard deviation issmaller. A local maximum can be found at ≈ 15 nm. The following measure-ments were hence executed at this thickness to avoid an artificial increase of theobtained standard deviations by an error of the measured specimen thickness.

High-resolution HAADF STEM images were acquired accordingly at a speci-men thickness of (16±2) nm, which was measured from the intensity in the GaNareas. The intensity was normalised to the incident intensity [14–16] and eval-uated in the same way as the simulated data before. An exemplary micrographis shown in Fig. 4a.

In the experiment, the intensity of atom columns varies even in pure GaN.This noise is primarily caused by small thickness variations and surface con-tamination. In the following, it was assumed that the noise caused by theseeffects is the same in the quaternary layers. However, it might be even larger inthe AlInGaN as selective etching causing stronger thickness variations is moreprobable there. Therefore, the noise with a standard deviation of 0.03 estimatedfrom a GaN area as the one marked red in Fig. 4b can be considered as a lowerbound for AlInGaN.

As standard deviations are added Pythagorean, the relative contribution ofthis noise to the standard deviation of 0.08 measured in the quaternary materialis less than 8%. The suchlike characterised noise was added to the simulateddata by adding Gaussian distributed random numbers with the according stan-dard deviation. The resulting histogram is shown in Fig. 4c in red. With thenoise added, the simulated data should be fully comparable to the experiment.Hence, the intensity ratio distribution was also determined from the measuredintensity of the AlInGaN layer with composition no.4 as marked in green inFig. 4b, leading to the green histogram in Fig 4c. Apparantly, both distri-

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Figure 4: Evaluation of the experimental HAADF STEM images: (a) is an overview of theinvestigated conventionally prepared specimen. The dotted rectangle marks the area, in whichthe high-resolution micrograph in (b) was taken. Averaging the image intensity over Voronoicells yields an experimental noise estimate. (c) shows the experimental histogram from theanalysis of the quaternary area marked by the green frame in (b) in direct comparison to thesimulation results with incorporated noise marked by the red frame.

butions are similar. This could also be confirmed by various statistical tests:Not only is the one-sample Kolmogorov-Smirnov-Lilliefors test accepting nor-mality of the experimental distribution with 20% significance, as it did for thesimulation.

The two-sample Kolmogorov-Smirnov test, which checks whether two sam-ples are from the same not necessarily Gaussian distribution, also confirms thatthe STEM intensity in the quaternary material has the same distribution asthe noise-incorporated simulation with an exceptional significance of 45%. In afurther statistical examination, the identity of the variances of simulation andexperiment was also accepted by a two-sample F-Test and Bartlett’s test, whichallow testing this identity, with 30% significance. The unity of this test resultsstrongly indicate the identity of the measured HAADF-intensity and the oneexpected for an entirely random alloy and hence a homogeneous composition inthe quaternary material.

However, as mentioned before, despite the very high significance with whichthe identity of distributions was accepted, the statistical power of the tests couldstill be small, if cluster-formation did not strongly alter the intensity-ratio dis-tribution. To check against an error of this kind, another STEM simulationwith a single cubic cluster with a side length of 3 nm with increased indiumconcentration of 40 at.% and reduced aluminum concentration of 20 at.% buriedinside a supercell of 15 nm thickness was conducted. Size and composition of thiscluster lies well in the range of inhomogeneities reported for AlInGaN [11, 13].The resulting image was evaluated as described above. The result is shown inFig. 5 in direct comparison to the random-alloy distribution. These histogramsare clearly different and in fact the two-sample Kolmogorov-Smirnov test rejectstheir identity and the one-sample Kolmogorov-Smirnov-Lilliefors test does notaccept Gaussian distribution of the intensity ratio obtained for the simulatedcluster, not even for a significance of only 1%. It can thus be concluded, thatthe statistical analysis of HAADF STEM data presented here powerful enoughand hence well-suited to exclude existence of nanometer-scale clusters with anindium concentration increased from approximately 20 at.% to 40 at.%. There-

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Figure 5: Simulated HAADF STEM imaging of an indium-rich cluster: The supercell shownin (a) contains an indium-rich cluster marked by the dotted frame. The cubic-shaped clusterhas a side length of 3 nm, the supercell is 15 nm high. The resulting histogram is shown ingreen in (b) in comparison to the distribution of a random alloy in black.

fore, the AlInGaN-layer investigated here is shown to be homogeneous to thisextent.

An attempt was also made to determine the indium and aluminum concen-trations by simultaneous evaluation of HAADF intensity and lattice strain mea-sured from the high-resolution STEM images as described by Grieb et al. [32].However, this method turned out to be less applicable for the AlInGaN mate-rial system as is illustrated in Fig. 6: Simulations as described above were con-ducted for various compositions from the two-dimensional concentration spaceas reference for the intensity. Additionally, the biaxial lattice strain in growthdirection was calculated from elasticity theory for comparison with the mea-sured strain. The isolines for both datasets, on which compositions with thesame HAADF intensity or the same strain, respectively, lie, are shown for afixed specimen thickness of 50 nm. This is a common thickness for quantitativeHAADF STEM measurements in the AlGaN/InGaN-system [15]. It becomesapparent that these isolines are nearly parallel, meaning that the informationwhich can be gained from the measurement of HAADF intensity and latticestrain is quasi equivalent. Even with both quantities measured the simultane-ous determination of both the aluminum and the indium concentration is there-fore impossible under experimental conditions as two non-equivalent pieces ofinformation would be necessary for this. Using this method the possible compo-sitional range is thus given by a narrow region along the isoline that correspondsto the measured normalised HAADF intensity.

This concentration range, however, was found to be in full agreement withthe other measurements in Tab. 1 as is illustrated in Fig 9. For the ternary

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Figure 6: Comparison of HAADF STEM and strain reference data: The isolines of STEMintensity (normalised to the incident probe intensity) simulated with the frozen-lattice methodand a specimen thickness of 50 nm are drawn in black, while the isolines of biaxial straincalculated by elasticity theory are plotted in red versus indium and aluminum concentrations.The red and black isolines run almost in parallel.

InGaN layer (composition no.1), where the prior knowledge of vanishing Alconcentration could be utilised to get an exact concentration, the indium con-centration was determined to be (11 ± 1) at.% and for the AlGaN layer (com-position no.5) (38± 1) at.% Al was found, which is in excellent agreement withthe other methods.

3.3. APT-Analysis

The specimens investigated in the previous section were also examined in acomparative APT study. The measurement conditions were optimised for thematerial system based on the findings of Mehrtens et al. [33] by cooling downthe specimen tip to 20 K and using a laser-pulse energy of 50 pJ at a pulse fre-quency of 100 kHz for a laser wavelength of 532 nm and a pulse length of ≈ 10 ps.60 million ions were detected during the entire measurement. Due to the op-timisation of acquisition parameters, a III:N-ratio of 52:48 could be achieved,which is close to the expected 1:1 ratio. The deficiency of measured nitrogen hasbeen reported to be due to the dissociation of complex ions between evaporationfrom the specimen and detection, causing inaccurate identification of incidentions [33, 34]. Fig. 7a shows an image of the reconstructed specimen. All fiveAlInGaN layers were detected entirely. The layer thicknesses and distances arein excellent agreement with the STEM micrographs. An atomic-concentration

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profile was extracted by averaging in lateral direction and for a bin width of0.2 nm in growth direction, which is presented in Fig. 7b. The average con-centration of each layer is also given in Tab. 1 and illustrated in Fig. 9, wherefair agreement with the EDX results within the according precisions becomesapparent.

The homogeneity was then statistically investigated similar to the STEMdata following Ref. [35]. The volume of each layer was divided into voxels,each containing a fixed number of detected ions. The concentration of eachion species was then calculated and the respective concentration distributioninside each layer was determined. The resulting histograms for Al-, In-, Ga-and N2-ions for layer no.4 and voxels containing 40 ions are displayed in Fig. 7cin comparison with the binomial distribution expected for a random alloy. Thevisibly good fit between both was tested by the chi-square test and acceptedwith a significance of 10% for all detected ion types. The test was repeated forvoxel sizes of 20, 100 and 200 ions, respectively, which corresponds to voxelswith approximate side lengths from 1.4 to 3.2 nm. It yielded an identity with arandom-alloy distribution with more than 5% significance in all cases. Similarresults were obtained for the other layers. Additionally, the radial distribu-tion around indium atoms was investigated by calculating the radially averagedconcentration as a function of the distance to a central indium atom and then av-eraging over all indium atoms. The result is shown in Fig. 7d for layer no. 4: Forindium-clustering, one would expect a significant increase in indium concentra-tion for small radial distances, which was not observed. The radial distributionis almost constant. The APT study hence does confirm the previous findings.All layers are found to be homogeneous on various scales.

To check the power of the previous test, a test structure with a singleAlInGaN-layer of a similar composition as no.4 was investigated with the sameparameters as before. Due to a pulsed MOVPE process, which involved an al-ternating injection of In-, Al- and Ga-precursors, this sample exhibited a stripyappearance in HAADF STEM images caused by monolayers of alternating dif-ferent compositions, as is shown in Fig. 8a. The stripes are also clearly visible inthe APT reconstruction in Fig. 8b, in which they were identified as fluctuationsof the aluminum concentration of approximately ±5 at.% with a simultaneouslyconstant indium content. This clearly inhomogeneous sample was also analysedby testing the concentration distributions against the random-alloy expectationwith the chi-square test. The corresponding histograms are shown in Fig. 8c.Random distribution of gallium and aluminum was clearly rejected, while it wasaccepted for indium and nitrogen with a significance of 20%. The test thereforeclearly proves its suitability to identify inhomogeneities caused by fluctuationsof the magnitude of 10 at.% on the sub-nanometer scale.

4. Summary

In conclusion, an investigation of the homogeneity of AlInGaN layers of dif-ferent concentrations by statistical means using EDX, HAADF STEM and APTwas presented. The layers were found to exhibit random-alloy distribution with

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Figure 7: Evaluation of the APT measurement: The reconstruction of the specimen is shownin (a). (b) displays the resulting concentration profile along the growth direction. In (c) thedistribution of various detected ions inside a layer (bars) is compared to the random-alloyexpectation (solid curves). (d) is a plot of the ionic concentration in dependence of the radialdistance from indium ions. Indications for non-random fluctuations are not found.

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Figure 8: APT evaluation of an inhomogeneous AlInGaN layer: Intensity fluctuations betweenatomic layers were observable in HAADF STEM micrographs as shown in (a), the reconstruc-tion in (b) revealed them to be caused by varying aluminum and gallium concentrations, whichcaused distinct deviation of measured (bars) and random-alloy (solid curves) distributions inthe histogram (c).

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high significances down to the sub-nanometer scale. The applicability of thetests to the two-dimensional HAADF STEM data was confirmed by additionalsimulations, in which the statistical power was demonstrated and proved to becomparable to corresponding analyses on three-dimensional APT reconstruc-tions.

The observed increase in width of the PL-emission peak can hence be de-ducted to stem solely from local concentration fluctuations inherent to a random-alloy distribution of elements. It can be furthermore concluded that, in thestudied composition range, the MOVPE parameters used for the growth of theinvestigated layers do indeed allow epitaxy of homogeneous quaternary AlIn-GaN without detectable phase separation. In respect to the previous reports ofindium cluster formation [10–13] this conclusion does not apply to any growthsetup in general. Nevertheless it is shown, that homogeneous MOVPE growthof AlInGaN for these concentrations is possible.

Finally, the quaternary concentrations were determined and consistent re-sults were attained as is also illustrated in Fig. 9, where the summarised resultsof all measurements presented here are seen to coincide within their precisions,though with HAADF STEM, the quaternary composition could not be deter-mined unambiguously, as a second non-equivalent information channel wouldbe needed. Nevertheless, it was demonstrated, that the statistical analysis ofSTEM micrographs by comparison to simulations is sufficiently powerful to ex-clude the presence of nm-scale chemical species clustering.

Acknowledgements

The research leading to these results has received funding from the Euro-pean Union Seventh Framework Programme under Grant Agreement 312483- ESTEEM2 (Integrated Infrastructure Initiative I3) and was supported bythe Deutsche Forschungsgemeinschaft under contracts RO2057/4-2, RO2057/8-1 and MU3660/1-1.

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Figure 9: Overview of the measured concentrations: The results of all investigated composi-tions from the different methods are marked with their respective errors (see Tab. 1). Theconcentration pairs of the quaternary compositions no.2 to 4, that are consistent with themeasured HAADF STEM intensity are drawn as black isolines (only reasonable part wasplotted for better readability). The XPS-data was taken from [20]. The values from EDX,HAADF STEM and APT coincide within their error bars.

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